Find the electric field strength vector, if the potential of this field has the form φ = a → · r → , where a → is a constant vector and r → is the radius vector of a point of the field.

Given potential, φ = a → · r → where, a is constant. Let a → = a x i ^ + a y j ^ + a z k ^ and r → = x i ^ + y j ^ + z k ^ Then, φ = a → · r → = a x x + a y y + a z z Thus, electric field, in terms of potential is, E → = - ∇ → φ where, ∇ → = ∂ ∂ x i ^ + ∂ ∂ y j ^ + ∂ ∂ z k ^ E → = - ∂ ∂ x i ^ + ∂ ∂ y j ^ + ∂ ∂ z k ^ a x x + a y y + a z z E → = - ∂ ∂ x a x x i ^ + ∂ ∂ y a y y j ^ + ∂ ∂ z a z z k ^ = - a x i ^ + a y j ^ + z k ^ = - a →

HARD

JEE Main

IMPORTANT

Earn 100

There are two thin wire rings each of radius $R$ , whose axes coincide. The charges of the rings are $q$ and $- q$ . Find the potential difference between the centres of the rings separated by a distance $a$ .

Important Questions on ELECTRODYNAMICS

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.31.

There is an infinitely long straight thread carrying a charge with linear density

λ = 0.40 μC m^{- 1}

. Calculate the potential difference between points

1

and

2

, if point

2

is removed,

η = 2.0

times farther from the thread than point

1

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.32.

Find the electric field potential and strength at the centre of a hemisphere of radius

R

, charged uniformly with the surface density

σ

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.33.

A very thin round plate of radius

R

carrying a uniform surface charge density

σ

is located in vacuum. Find the electric field potential and strength along the planet's axis as a function of a distance

l

from its centre. Investigate the obtained expression at

l \to 0

and

l ≫ R .

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.34.

Find the potential

φ

at the edge of a thin disc of radius

R

carrying the uniformly distributed charge with surface density

σ

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.35.

Find the electric field strength vector, if the potential of this field has the form

φ = \vec{a} \cdot \vec{r}

, where

\vec{a}

is a constant vector and

\vec{r}

is the radius vector of a point of the field.

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.36.

Determine the electric field strength vector, if the potential of this field depends on $x$ and $y$ coordinates as,
(a) $φ = a (x^{2} - y^{2});$ (b) $φ = a x y,$

where $a$ is a constant. Draw the approximate shape of these fields using lines of force. (In the $x, y$ plane)

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.37.

The potential of a certain electrostatic field has the form

φ = a (x^{2} + y^{2}) + b z^{2}

, where

a

and

b

are constants. Find the magnitude and direction of the electric field strength vector. What shape have the equipotential surfaces, in the following cases:
(a)

a > 0, b > 0;

(b)

a > 0, b < 0

HARD

JEE Main

IMPORTANT

Problems in General Physics>Chapter 3 - ELECTRODYNAMICS>CONSTANT ELECTRIC FIELD IN VACUUM>Q 3.38.

A charge

q

is uniformly distributed over the volume of a sphere of radius

R

. Assuming the permittivity to be equal to unity throughout, find the potential
(a) at the centre of the sphere;
(b) inside the sphere, as a function of the distance

r

from its centre.

There are two thin wire rings each of radius R, whose axes coincide. The charges of the rings are q and -q. Find the potential difference between the centres of the rings separated by a distance a.

Important Questions on ELECTRODYNAMICS

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There are two thin wire rings each of radius $R$ , whose axes coincide. The charges of the rings are $q$ and $- q$ . Find the potential difference between the centres of the rings separated by a distance $a$ .